There is a bad smell in my house (like from something rotten) but I can’t find the source. Am I allowed to recite Brochos in it?

You can spray the area where you’re standing with air freshener and then make a Bracha.

Sources:

עפ”י שוע”ר עט סעי’ ו וסי’ פה סעי’ א ופתחי עולם סי’ עט ס”ק ט.